Thanks all for the explanations. I guess the consensus is Carter was crazed out of his mind, and acting irrationally, and B it is needed by the script to wrap up all the impediments to the MC getting what he really wants, all in a single fast-moving scene.
It could have been a lot worse. Imagine the rage if the update ended with Emma and Zac holding hands and/or kissing in the movie theater, haha.
I think it's been explained.
Carter never intended to face the MC tonight. He intended for MC to find Emma's dead body. Her and Zac's murders were supposed to look like a random act of violence or mugging gone wrong.
His plan got thrown out the window when MC arrived at record speed.
Now he's cornered, and MC threatens that if he kills Emma, MC will immediately draw his gun and kill him.
As much as Carter hates MC, he wants to live.
Instead MC offers to face him in close quarters combat if he releases Emma. Carter likes this idea. Sure the MC is special forces, but Carter has a knife and he's got some training of his own. He thinks this gives him a good chance of winning, and then he can go kill Charlotte and Emma to get rid of the witnesses and stage the scene to his liking.
Lucky for MC, the skill difference between them was bigger than Carter estimated but....all things considered...Carter made the smartest choice he could make in that moment.
MAYBE he should have drawn his own gun and tried to kill the MC but then it becomes a quickdraw contest and he might not have liked his odds in that sort of fight. It also becomes an accuracy contest and cops don't spend as much time on the shooting range as you might think.
He also might not have had his gun on him. Unlikely, but possible. He also might not have had a gun at all. As others have mentioned there are many hints suggesting this story is set in the UK, or some other Europe-inspired country. Many European countries don't provide guns as standard issue weapons to their police
Knife Vs Barehands was his best chance of winning. But it was still only a chance. A chance that did not land in his favor.